On the Methods of One-Dimensional Auxiliary Problems and of Domain Partitioning: Their Application to Lower Bounds for the Eigenvalues of Schrodinger's Equation

1964 ◽  
Vol 43 (1-4) ◽  
pp. 15-26 ◽  
Author(s):  
Joseph Hersch
Keyword(s):  
Lower Bounds ◽  
One Dimensional ◽  
Schrödinger’S Equation ◽  
Domain Partitioning ◽  
Schrödinger's Equation

scholarly journals On combined optical solitons of the one-dimensional Schrödinger’s equation with time dependent coefficients

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 65-68 ◽  
Author(s):  
Bulent Kilic ◽  
Mustafa Inc ◽  
Dumitru Baleanu
Keyword(s):  
Soliton Solutions ◽  
First Integral ◽  
Optical Solitons ◽  
Time Dependent ◽  
Ansatz Method ◽  
One Dimensional ◽  
Optical Metamaterials ◽  
Schrödinger’S Equation ◽  
The One ◽  
Schrödinger's Equation

AbstractThis paper integrates dispersive optical solitons in special optical metamaterials with a time dependent coefficient. We obtained some optical solitons of the aforementioned equation. It is shown that the examined dependent coefficients are affected by the velocity of the wave. The first integral method (FIM) and ansatz method are applied to reach the optical soliton solutions of the one-dimensional nonlinear Schrödinger’s equation (NLSE) with time dependent coefficients.

scholarly journals Exact and approximate solutions of Schrödinger’s equation for a class of trigonometric potentials

Open Physics ◽  
2013 ◽  
Vol 11 (1) ◽  
Author(s):  
Hakan Ciftci ◽  
Richard Hall ◽  
Nasser Saad
Keyword(s):  
Differential Equation ◽  
Coordinate Transformation ◽  
Iteration Method ◽  
Order Differential Equation ◽  
Approximate Solutions ◽  
Asymptotic Iteration Method ◽  
Perturbation Expansions ◽  
One Dimensional ◽  
Schrödinger’S Equation ◽  
Schrödinger's Equation

AbstractThe asymptotic iteration method is used to find exact and approximate solutions of Schrödinger’s equation for a number of one-dimensional trigonometric potentials (sine-squared, double-cosine, tangent-squared, and complex cotangent). Analytic and approximate solutions are obtained by first using a coordinate transformation to reduce the Schrödinger equation to a second-order differential equation with an appropriate form. The asymptotic iteration method is also employed indirectly to obtain the terms in perturbation expansions, both for the energies and for the corresponding eigenfunctions.

Lower Bounds for Eigenvalues of Schrödinger's Equation

1961 ◽  
Vol 124 (2) ◽  
pp. 483-492 ◽  
Author(s):  
Norman W. Bazley ◽  
David W. Fox
Keyword(s):  
Lower Bounds ◽  
Schrödinger’S Equation ◽  
Schrödinger's Equation

Numerically Efficient Computation of Eigensolution Spectrum in One-Dimensional Heterostructures

1998 ◽  
Vol 09 (07) ◽  
pp. 927-934 ◽  
Author(s):  
F. Farrelly ◽  
A. Petri
Keyword(s):  
Transfer Matrix ◽  
Density Of States ◽  
Spatial Behavior ◽  
Efficient Computation ◽  
Matrix Methods ◽  
One Dimensional ◽  
Schrödinger’S Equation ◽  
Schrödinger's Equation

We describe a method that allows an efficient determination of the density of states of one-dimensional heterostructures. We show that the propagation of an appropriate vector through the structure together with the use of the node theorem is much more effective than transfer matrix methods in those cases in which highly degenerate spectra are present. As a by-product, spatial behavior of solutions is also easily obtained. A case of elastic propagation is discussed in detail and application to Schrödinger's equation is presented.

scholarly journals A New Explicit Four-Step Symmetric Method for Solving Schrödinger’s Equation

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1124 ◽  
Author(s):  
Saleem Obaidat ◽  
Said Mesloub
Keyword(s):  
Stability Analysis ◽  
Linear Method ◽  
Phase Lag ◽  
One Dimensional ◽  
Schrödinger’S Equation ◽  
First Derivative ◽  
Algebraic Order ◽  
The One ◽  
Schrödinger's Equation ◽  
Symmetric Method

In this article we have developed a new explicit four-step linear method of fourth algebraic order with vanished phase-lag and its first derivative. The efficiency of the method is tested by solving effectively the one-dimensional time independent Schrödinger’s equation. The error and stability analysis are studied. Also, the new method is compared with other methods in the literature. It is found that this method is more efficient than these methods.

Schrödinger’s Equation on a One-Dimensional Lattice with Weak Disorder

1993 ◽  
Vol 53 (5) ◽  
pp. 1210-1252 ◽  
Author(s):  
R. Kuske ◽  
Z. Schuss ◽  
I. Goldhirsch ◽  
S. H. Norskowicz
Keyword(s):  
Weak Disorder ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Schrödinger’S Equation ◽  
Schrödinger's Equation
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